A fast algorithm for particle simulations
Journal of Computational Physics
Simulating the motion of flexible pulp fibres using the immersed boundary method
Journal of Computational Physics
A Generalized Fast Multipole Method for Nonoscillatory Kernels
SIAM Journal on Scientific Computing
Simulations of the Whirling Instability by the Immersed Boundary Method
SIAM Journal on Scientific Computing
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
An iterative matrix-free method in implicit immersed boundary/continuum methods
Computers and Structures
Simulation of flexible filaments in a uniform flow by the immersed boundary method
Journal of Computational Physics
Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces
Journal of Computational Physics
Journal of Computational Physics
A velocity decomposition approach for moving interfaces in viscous fluids
Journal of Computational Physics
Journal of Computational Physics
Dynamics of multicomponent vesicles in a viscous fluid
Journal of Computational Physics
Modeling simple locomotors in Stokes flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A fast algorithm for simulating vesicle flows in three dimensions
Journal of Computational Physics
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
Hi-index | 31.51 |
The dynamics of slender filaments or fibers suspended in Stokesian fluids are fundamental to understanding many flows arising in physics, biology and engineering. Such filaments can have aspect ratios of length to radius ranging from a few tens to several thousands. Full discretizations of such 3D flows are very costly. Instead, we employ a nonlocal slender body theory that yields an integral equation, along the filament centerline, relating the force exerted on the body to the filament velocity. This hydrodynamical description takes into account the effect of the filament on the fluid, and is extended to capture the interaction of multiple filaments as mediated by the intervening fluid. We consider filaments that are inextensible and elastic. Replacing the force in the slender body integral equation by an explicit expression that uses Euler-Bernoulli theory to model bending and tensile forces yields an integral expression for the velocity of the filament centerlines, coupled to auxiliary integro-differential equations for the filament tensions. Based on a regularized version of these slender body equations that is asymptotically equivalent to the original formulation, we construct a numerical method which uses a combination of finite differences, implicit time-stepping to avoid severe stability constraints, and special quadrature methods for nearly singular integrals. We present simulations of single flexible filaments, as well as multiple interacting filaments, evolving in a background shear flow. These simulations show shear induced buckling and relaxation of the filaments, leading to the storage and release of elastic energy. These dynamics are responsible for the development of positive first normal stress differences, commonly associated with visco-elastic fluids that are suspensions of microscopic elastic fibers.